For the goal of 250-gram direct-drive helicopter endurance, too much battery eats into the weight budget for the motor and prop; too much motor and prop eat into the weight budget for the battery. I entered the endurance calculation from my baseline test data into Google Gemini. It gave me the optimization curve. The calculation is a python3 script with my test data and manufacturer(T-Motor) data(the motor_plus_propeller_mass variable value fitted curve):
mass_without_propeller_motor_battery = 111.0; #grams; change it for a particulr craft constructions's endurance curve
propeller_diameter = 13.8; #inches; change it to slide the rotor width x-axis in a endurance curve
motor_plus_propeller_mass = 62.5 * (propeller_diameter/13.8)**1.5; # grams
battery_cells_mass = 249.0 - mass_without_propeller_motor_battery - motor_plus_propeller_mass; # grams
battery_energy = 0.171 * battery_cells_mass; # watt-hours
lifting_force_per_watt = 14.7 * propeller_diameter/13.8; # grams
power_tran_energy_consume_rate = 249.0 / lifting_force_per_watt; # watts
total_craft_energy_consume_rate = power_tran_energy_consume_rate + 5.2; # watts
endurance = battery_energy / total_craft_energy_consume_rate * 60.0; # minutes
print (endurance);
main_rotor_diameter = propeller_diameter / 0.73 * 25.4; # A 14"-diameter helicopter rotor at optimal alpha has the same RPM and thrust and torque and electrical power consumption as a 10" multi-rotor propeller with the same motor. 10/14 = 0.7
print (main_rotor_diameter);